Quickly finishes meal and spruces up first three offices (8,3)

I believe the answer is:

polishes off

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'quickly finishes' is the definition.
'polishes off' can be an answer for 'finishes' ('polish off' can be a synonym of 'finish'). I am not certain of the 'quickly' bit.

I don't understand the rest of the clue.

Can you help me to learn more?

I've seen this clue in The Irish Times.

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